Year: 2018
Author: Alain Miranville, Charbel Wehbe
Journal of Mathematical Study, Vol. 51 (2018), Iss. 4 : pp. 337–376
Abstract
We consider a phase field model based on a generalization of the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Neumann boundary conditions. The originality here, compared with previous works, is that we obtain global in time and dissipative estimates, so that, in particular, we prove, in one and two space dimensions, the existence of a unique solution which is strictly separated from the singularities of the nonlinear term, as well as the existence of the finite-dimensional global attractor and of exponential attractors. In three space dimensions, we prove the existence of a solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v51n4.18.01
Journal of Mathematical Study, Vol. 51 (2018), Iss. 4 : pp. 337–376
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 40
Keywords: Caginalp phase-field system Maxwell-Cattaneo law logarithmic potential Neumann boundary conditions well-posedness global attractor exponential attractor.